Denoising with three dimensional fourier transform for three dimensional images, including image sequences

ABSTRACT

A method of mitigating noise in source image data representing pixels of a 3-D image. The “3-D image” may be any type of 3-D image, regardless of whether the third dimension is spatial, temporal, or some other parameter. The 3-D image is divided into three-dimensional chunks of pixels. These chunks are apodized and a three-dimensional Fourier transform is performed on each chunk, thereby producing a three-dimensional spectrum of each chunk. The transformed chunks are processed to estimate a noise floor based on spectral values of the pixels within each chunk. A noise threshold is then determined, and the spectrum of each chunk is filtered with a denoising filter based on the noise threshold. The chunks are then inverse transformed, and recombined into a denoised 3-D image.

GOVERNMENT SUPPORT CLAUSE

This invention was made with United States Government Support underPrime Contract Nos. NNX16AF98G and NNX16AG98G, funded by NASA GoddardSpace Flight Center. The Government has certain rights in thisinvention.

TECHNICAL FIELD OF THE INVENTION

This invention relates to image processing, and more particularly to amethod of removing noise using adaptive filtering in the Fourier domain.

BACKGROUND OF THE INVENTION

Many scientific, medical, or other still images and image sequences areconveyed from an image sensor via a signal that contains additive noisethat contaminates the signal. The noise takes the form of a randomvariable, typically approximately normally distributed, that is sampledindependently at different locations in the image. These locations canvary in size from single pixels to resolution elements. The noisedistribution can be independent of the image value (“pure additivenoise”) or dependent on the image value (“variable additive noise”).

An example of pure additive noise is read noise of a digital imagedetector. Another example of pure additive noise is randomelectromagnetic interference in a digital image detector.

An example of variable additive noise is photon shot noise associatedwith the Poisson statistics of photon counting in modern detectors,which varies as the square root of total photon count. Another exampleis film grain, which affects conventional photographic images and moviesin a complex, but predictable, manner that depends on the photographicprocess and the local image value.

Pure and variable additive noise can significantly limit both thedynamic range and resolution of an image. Some examples, without impliedlimitation, include: low-light photography and cinematography of allsorts; medical imaging including magnetic resonance imaging, X-rayimaging or fluoroscopy, and computed-tomography scans; andastrophotography and astrophysical imaging.

Various techniques exist to reduce noise both in still images and inimage sequences. For image sequences, such as video, conventionaldenoising methods use Fourier transforms, and also use a motionestimation process that estimates the degree of motion in portions ofthe sequenced images. The motion estimation process co-aligns featuresthat are present in adjacent frames of the sequence, and makes use oftemporal redundancy. However, the motion estimation process is ill-posedand imposes known difficulties. It also limits the use of the noisereduction technique on tomographic data or other non-temporal data setsthat may be represented as a sequence of images.

Conventional denoising methods for image sequences sometimes refer to“3-D denoising”. However, this may mean 2-D transforms followed by 1-Dtransforms, and these methods include the above-described motionestimation. This approach is described in U.S. Pat. No. 8,619,881, andother references.

BRIEF DESCRIPTION OF THE DRAWINGS

A more complete understanding of the present embodiments and advantagesthereof may be acquired by referring to the following description takenin conjunction with the accompanying drawings, in which like referencenumbers indicate like features, and wherein:

FIG. 1 illustrates an imaging system with a denoising process inaccordance with the invention.

FIG. 2 illustrates the various subprocesses of the denoising process.

FIG. 3 illustrates the “chunking” process for an image sequence, inwhich time is treated as a third dimension.

FIGS. 4-15 illustrate mathematically, how the denoising process isimplemented.

DETAILED DESCRIPTION OF THE INVENTION

Overview

The following description is directed to an image denoising method thatfinds the statistical signature of noise in the three-dimensionalFourier domain, in small localized “chunks” of 3-D images, as definedherein. The method makes use of coherence of image features across allthree dimensions, to discriminate between a valid image signal andnoise. The method does not require motion estimation betweentwo-dimensional image frames.

In what is conventionally thought of as a “3-D image”, the thirddimension is spatial, e.g. an (x, y, z) image. For example, in atomographic data set, the third dimension would represent the thirdspatial dimension.

However, for purposes of this description, the term “3-D image” is alsoused to include an image sequence or other ordered sets of images inwhich the third dimension is not necessarily spatial. An “imagesequence” can be broadly defined as an ordered set of 2-D images, withsequence number being the third dimension. For example, an imagesequence could represent a sequence of frames in a movie or video, withthe third dimension being time, e.g. an (x, y, t) image.

Thus, for purposes of this description, 3-D images can be “spatial 3-Dimages” or “time 3-D images”, or other types of “3-D images”, in whichthe third dimension could be some other parametric dimension, such as aspectral dimension. For convenience, the term “image” is sometimes usedherein, and it should be clear from context that “3-D image” as definedabove is meant.

The “3-D image” may be semi-infinite along the third dimension, such asa data stream, or may have well defined boundaries known in advance,such as a finite length video or a well defined 3-D data set.

The 3-D image structure is exploited without reference to specificfeatures or to bulk motion of the image subject through the image plane.As compared to the 2-D transform processing referred to in theBackground, for time 3-D images, additional noise reduction for the 3-Dtransform processing described herein arises because the method exploitsfeature coherence across both time and space. The method requires onlythat a moving or evolving object have a discrete Fourier spectrum thatis distinguishable in amplitude from the background noise field, withoutregard for the shape of the feature or the particulars of its evolutionacross image frames.

3-D Denoising System and Method

FIG. 1 illustrates one embodiment of the invention for the tangibleresult of displaying a denoised image. Other embodiments are discussedbelow.

System 10 is an imaging display system, with a denoising process 12 inaccordance with the invention. It should be understood that, althoughnot shown, various other processes may be performed on the image data;only the processing relevant to the invention is shown.

The detector 11 may be any type of image gathering device. The imagedata, Im, is three-dimensional. The 3-D images comprise, in two of thethree dimensions, a 2-D “image frame” of pixels, each pixel having avertical position, a horizontal position, and one or more pixel datavalues. In a monochromatic image, each pixel has a brightness value. Acolor image might have three values (red, green, and blue brightnesses)at each pixel location. Similarly, a hyperspectral image might havemultiple pixel values. Multiple pixel values might be treatedindependently by the method described herein, or be combined through amathematical transformation before being treated. As discussed above,the third pixel dimension can be time, space, or some other parameter.

The denoising process 12, explained in detail herein, mitigates noisewithin the 3-D image. It is a computer-implemented process, and process12 includes processing hardware and software appropriate to implementthe method described herein. Process 12 may be integrated with a morecomprehensive image processing system for various other image processingand buffering steps.

The denoising process 12 receives noisy 3-D image data, performs thedenoising process, and outputs denoised 3-D image data. In theembodiment of FIG. 1, the data is then delivered to a display 13, whichmay be any device that generates a tangible output, such as a monitor orprinter. This output is data representing a denoised 3-D image, that is,the original image data has had its noise components reduced.

In other embodiments, the denoised data may be delivered to some otheroutput device or to a process for further processing. Denoising of 3-Dimages can help prepare the 3-D image data for many types of furtherprocessing. In addition to direct display, the image data can be inputto data compression processing and stored or transmitted for laterdisplay. Examples of other applications are for optical flowmeasurement, tomographic reconstruction analysis, photometric orcolorimetric analysis, timing analysis, and further feature enhancementvia processes such as unsharp masking. In general, the eventual tangibleresult of the 3-D image denoising process can be for direct visualgraphic display or any other quantitative analysis.

FIG. 2 illustrates the 3-D image denoising process 12 in further detail.

In a blocking process 201, the 3-D image is broken into 3-D overlapping“chunks” of size n1×n2×n3. As described above, for time 3-D images, thethird dimension is time. In other words, each pixel of the imagesequence is considered to have the two dimensions of a 2-D image andadditionally a third dimension, which refers to position in time. Forother 3-D images, the third dimension could be a spatial dimension. Or,the third dimension could be some other parameter dimensiondifferentiating images in a data set of related image frames.

The chunks need not necessarily be the same size in all threedimensions. In other words, in some implementations, n1, and n2 and n3may be equal. However, no numerical relation between this size of thesechunk dimensions is necessary.

The chunks are “aligned” in all dimensions. Each chunk is taken from thesame horizontal and vertical (x, y) position in the frames. For spatial3-D (x, y, z) images, the chunks have the “z” positions corresponding tothat (x, y) position in successive frames. For time 3-D images (x, y,t), the chunks have the “t” sequence corresponding to that (x, y)position in successive frames.

An example of blocking process 201 is subsampling a 3-D image data setinto 12×12×12 (cubical) pixel chunks, staggered every three pixels. Thesize of the chunks for a particular application may be varied to takeadvantage of the particular spectral characteristics of an image.

FIG. 3 illustrates the chunking process 201 for a 3-D image comprising nframes 30. For time 3-D images, the 3-D (x, y, t) chunks 31 are takenfrom successive image frames of an image sequence. In the example ofFIG. 3, the chunks are cubical, such that each chunk 31 is n×n×n pixels.Using the 12×12×12 example, the time dimension of each chunk would callfor including pixels from 12 successive image frames. Although notexplicitly shown in FIG. 3, neighboring chunks are overlapping to enableapodization of each chunk.

The overall concept of using “chunks” is that of local neighborhoodnoise filtering. Features in an image tend to have a concentratedFourier spectrum. In each chunk of pixels containing noisy butdiscernable structure (features), typically only a few Fouriercomponents will contain nearly all the Fourier energy in a feature. Thisis in contrast to uncorrelated per-pixel noise, which in notconcentrated by the Fourier transform. As a result, features become moreconcentrated in the Fourier domain, compared to noise. Thisconcentration can be used to retain features, while attenuating orrejecting components containing mainly noise. The denoising is locallyadapted to preserve the data signal in each neighborhood of the 3-Dimage.

Also, in the blocking process 201, the chunks are individually apodized.Apodization brings the edges of each image chunk smoothly to zero in away that minimizes edge effects on the Fourier spectrum. It isaccomplished by multiplying each image chunk by a windowing function,which convolves the Fourier spectrum.

For example, each chunk may be multiplied by the Hanning (sin ^2) windowfunction. The Hanning window has Fourier power only in the zero andfirst nonzero frequency in each axis, and therefore minimally spreadsthe spectrum of the apodized image. In practice, apodization may beapplied both before and after filtering.

In the transform process 202, each chunk is Fourier-transformed usingthe real-number FFT (or, equivalently, discrete cosine transformed) toproduce a 3-D image spectrum. This 3-D image spectrum is the combinedspectrum of any local image elements, together with image noise.

Adaptations can be made depending on the application. For example,rather than the full complex discrete Fourier transform, it may besufficient to use the real discrete Fourier transform or, equivalently,the discrete cosine transform. All such transforms are deemed equivalentfor purposes of this description.

The noise estimation process 203 is essentially estimation of a noise“floor” to be used in a denoising filter. As explained below, havingdetermined a noise floor, a noise threshold and a denoising filter canbe derived.

In one approach, described in detail below, the noise floor isdetermined a posteriori from local image characteristics inside eachchunk. A “constant-across-images spectrum” derived from ensemblestatistics of the transformed chunk spectra can be used as one factor ofnoise estimation.

Parametric functions that describe how the noise is thought to varyacross image brightness values can also be used for noise estimation,and determined either a priori or a posteriori. For example, in sometypes of 3-D images, shot noise varies as the square root of brightness.Other detector noise sources, such as electromagnetic interference orfilm grain, may vary as some other function of the image brightness.Similarly, noise sources may depend on location within the image. Forexample, shot noise may vary in a known way across the image as a resultof optical vignetting or other detection effect.

Alternatively, a noise floor may be determined by some other means. Asan example, the noise floor may be a constant value for simple noisegating.

In the noise filter process 204, the spectrum of each separate chunk ismodified according to a denoising filter function.

FIG. 4 illustrates the adaptive filter concept—a collection of filterfunctions, F′_(i), that are applied to corresponding image chunks,Im_(i), or their Fourier transformed counterparts, Im′_(i). The indexnotation “i” distinguishes between different filter functions, each ofwhich may be calculated from the determined noise spectrum and thecorresponding image chunk.

For example, as illustrated in FIG. 5, a simple noise gating filter mayzero those components that do not rise above an identified noise floor.The threshold function, T′_(i), is based on noise floor levels.

Alternatively, as illustrated in FIG. 6, a Wiener filter may be used toscale each component according to its amplitude relative to the computedfloor value for that component in that particular chunk. The Wienerfilter tends to roll off filter response more gradually, but may admitmore noise at a given threshold level.

In simple denoising functions, the threshold level, T, may be equal tothe noise floor, N, which itself may be fixed or parametrically adjustedas described below. Or, T may be calculated as an ad hoc factor, γ_(i)times a noise floor, N, that is either fixed or parametrically adjusted.The ad hoc factor, γ_(i) biases the filtering between preserving themost signal possible or rejecting the most noise possible.

FIG. 7 illustrated the threshold function, T, as a function of both anad hoc factor and a parametrically adjusted noise spectrum, N′(k_(x),k_(y), ω). A detailed discussion of this noise model is set out below.

In the image reconstruction process 205, the chunks are recombined intoa facsimile of the original image data, via inverse-transformation andweighted summing. If the windowing function is the Hanning function, theoriginal 3-D image may be recreated by overlapping chunks in such a waythat their window functions sum to unity, avoiding the need toaccumulate a weighted sum.

For an image stream, the process is repeated for successive imageframes. Overlapping chunks of pixels are repeatedly generated andprocessed as described above. Because the denoising method is a localprocess, once a noise floor or other denoising function is determined,the method may be used as a stream or pipeline process, acting on asemi-infinite 3-D image as individual 2-D image plane frames. In otherwords, for long image sequences, the chunking, transforming, filtering,and reconstructing process may be repeated in the time dimension, untila desired length of the image sequence is denoised.

Several approaches are possible to overcome any edge effects induced inthe apodization or windowing functions by the transform-domainfiltering. A first approach is to oversample the data with multipleoverlapping chunks containing each individual data point. A secondapproach is to hybridize the windowing function with a secondregularization step of apodization after the filtering step.

A feature of the method is that it does not rely on motion compensation,nor on the existence of a nearly unchanging feature with a well-definedmotion vector. Thus, the method is suitable not only for video and otherimage sequences, but for 3-D image data sets such as tomographic images.

The above-described method exploits the well-known property of theFourier transform that structured objects such as image features arelocalized (concentrated) in Fourier space, while random variables suchas noise are not. This permits, under many circumstances, cleanseparation of image features from noise. By preserving image Fouriercomponents that rise above a predetermined or calculated noise floor,and rejecting or attenuating those that do not, the method rejects noisewhile retaining important image data.

The resulting preserved features are photometrically accurate in thesense that the method preserves all feature information that can bediscerned above the noise level. This results in images that havesignificantly less noise but retain the full spatial and, whererelevant, temporal resolution of the original unprocessed image data. Bycomparison, conventional de-noising methods, such as blurring ortemporal averaging, often trade resolution for dynamic range byattenuating all components in the high spatial and temporal frequencyportion of Fourier space, whether or not those components containsignificant amounts of information above the noise floor.

The above-above described method may be compared in effectiveness tosimple blurring by averaging the value in regions equivalent to the“chunks” of the above method. If a chunk contains N pixels, and thenoise is sampled independently in each pixel, then blurring by averagingall pixels in a chunk will typically reduce the noise signal by factorof sqrt(N). Applying the above method to the same region may only rejectapproximately half of the Fourier terms, resulting in approximately 70%of the noise reduction that simple blurring would produce, while stillpreserving full resolution image structure.

Processing image sequences as 3-D chunks offers major gains in noisereduction compared to processing each image independently. This isbecause 3-D chunks with length scale of L pixels typically reduce thenoise by L raised to the 3/2 power. In contrast, 2-D chunks with lengthscale L pixels reduce it only by L raised to the 1st power.

The method relies only on the existence of coherent structure thatpersists between image planes, without regard to the nature of thatstructure. For example, features that distort, fade, move, or rotatebetween image planes will produce a coherent set of enhancedcoefficients in the corresponding Fourier-transformed chunks, eventhough the particular coefficients that are enhanced vary with thefeature's behavior. This permits the method to differentiate betweencoherent signal and incoherent noise, even though neither the featurenor its evolution are specifically identified.

The above method fits into the broad category of “adaptive filtering”,with filters that change their characteristics across an image accordingto statistics of the image itself. It is reminiscent of methods used inJPEG compression, with important distinctions. First, JPEG compressionis intended to compress the data, not to improve it, and thereforeattenuates or degrades the representation of Fourier components that aredeemed nonessential, rather than attenuating or eliminating componentsthat are deemed to be noise. Second, JPEG compression does not operateon apodized, re-merged windows but rather on isolated chunks withoutapodization. Third, JPEG compression operates on 2-D images.

Estimating Noise Level from Noise Spectrum

As illustrated in FIG. 8, 3-D images are mappings Im: Z³→R, where thedomain runs over pixel coordinates and the range describes imagebrightness. In general, practical image sequence data (after correctionfor fixed detector effects, i.e. “flat-fielding”) contain at leastadditive and shot noise. In the example of FIG. 8, Im is a time 3-Dimage, Im₀ is the “ideal” noise-free dataset, N_(a) is an additive“background noise” term independent of Im₀, N_(s) is an additive “shotnoise” term that depends on Im₀, and N_(other) is noise from all othersources.

Simple threshold noise-gate filtering, based on a simple threshold ofcomponent amplitude, to remove N_(a) can be adapted to 3-D images, bychunking and Fourier transforming in three dimensions as describedabove. However, this simpler method is not readily applicable to manyimage applications, because uniform additive noise is often not thedominant contaminant of image data. In a large class of images, N_(s)rather than N_(a), dominates the noise field in the image; N_(a) andN_(other) can be neglected. Because N_(s) depends on the value of Im₀,the simple form of noise-gate filtering is not sufficient as it is forN_(a).

Shot noise arises from the Poisson-distribution statistics of countingdiscrete quanta—photons, photoelectrons, or other quantized elementsthat depend on the detection technology. Shot noise is a randomvariable, sampled once per pixel, whose value depends also on the localvalue of the source image.

FIG. 9 represents an estimate of shot noise, when the number of quantais high and the Poisson distribution is well approximated by a Gaussiandistribution. The constant α is an instrument-dependent constant, andG(x, y, t) is a random variable with a fixed Gaussian distribution ofmean 0 and variance 1.

The equation of FIG. 9 is particularly useful because it divides shotnoise into three components, two of which can be well characterized. Theα coefficient is a constant of the instrument, and can be reconstructedfrom flat-field images or directly from image data. The function G(x, y,t) is a standard tool of statistical analysis.

FIG. 10 illustrates how, by Fourier transforming the equation of FIG. 9,it is possible to estimate the spectral amplitude of the noise in theimage.

But G′(kx, ky, ω) is constant across Fourier space, since G(x, y, t) isa normal random variable. For a broad class of scenes, thezero-frequency component of the Fourier transform dominates the spectrumand the F (square root) term can be treated as a delta function.

From the foregoing, the approximation of FIG. 11 is possible. Theconstant β (referred to herein as a “constant-across-images spectrum”)is a constant-across-images spectrum that is characteristic of thedetector that acquired the image. The fact that the sum of the noiseterm over many pixels is approximately zero, is used to replace Im₀ withIm under the radical.

The equation of FIG. 11 is useful because it estimates the noiseamplitude in an image, if β can be determined. In principle, β can bedetermined a priori from the absolute sensitivity of the detector.However, β can also be determined by a posteriori analysis of the data.This is accomplished by breaking a full dataset Im(x, y, t) intomultiple chunks Im_(i), and searching for a minimum scaled spectrum foreach one.

FIG. 12 illustrates the result of Fourier transforming the equation ofFIG. 8 with N_(a) and N_(other) neglected, and substituting the equationof FIG. 11, for each chunk index i.

Solving for β gives the equation of FIG. 13. The difference in thenumerator is the (unknown) Fourier spectrum of the shot noise, and thebar over Im_(i) in the denominator indicates summing the square root ofeach (positive-definite) pixel value.

Across a large population of image chunks, the estimates of βi at agiven location in Fourier space will vary from a minimum where the noisespectrum sample at that particular point is near zero, to a maximumwhere the local sampled value of the shot noise is much larger than thecorresponding Fourier component Im′₀. But structured images containingcoherent features are dominated by a few sparse Fourier components whereIm′₀(k_(x), k_(y), ω)≈Im′ (k_(g), k_(y), ω). Because the shot noise is arandom variable, its Fourier amplitude is more nearly constantthroughout the space, and most Fourier components are instead dominatedby the noise: |Im′₀|«|Im′(k_(x), k_(y), ω)|. Because the latter is themore common case, the median value of β_(i) across many image samples isa good estimator of the noise spectrum.

From the foregoing, β can be approximated as shown in FIG. 14. Thisapproximation depends only on the statistics across image chunks of theFourier spectrum in the original data set.

The calculated value of β_(approx) allows estimation of the noise levelacross all regions of an image sequence dominated by conventional shotnoise, per the equation of FIG. 11. Referring to both FIGS. 7 and 11,the approximation of β provides a basis for the threshold functions,T_(i), in the denoising filters described above.

The approximation of β_(i) in FIG. 14 requires that a significantfraction of the Fourier space be noise dominated, e.g., at least half ofall chunks. This is typically the case in image sequences that havedirect visual evidence of shot noise. However, for images that are morehighly structured, the median could be replaced with a lower percentilevalue.

The above-described noise estimation process avoids a need to detectscene changes (motion estimation) as do some conventional denoisingtechniques. The noise performance of the detector is parameterized. As aresult, multiple image frames taken with the same exposure and opticalsettings of the detector, will have the same parametric noiseperformance. The above-described β parameter is a constant of thedetector.

As stated in the Background, shot noise is dependent on the value of theimage, and is distinguishable from pure additive noise, which isindependent of the image value.

FIG. 15 illustrates how, for image-independent additive noise, one canestimate the noise level with a simpler calculation of a constant levelacross image chunks. As with the equation of FIG. 14, for images inwhich noise is low or that are highly structured, the median can bereplaced with a lower percentile across image samples.

The noise models of FIGS. 14 and 15 are two examples, for shot noise andfor constant additive noise, respectively, of how noise models can bederived from the spectral values of the pixel within image chunks. Inboth methods, the noise level is an approximation that is derived fromstatistics across image chunks of the Fourier spectrum in the originaldata set.

The same concepts can be used to derive noise estimations for differentkinds of noise. As another example, the noise estimator could compriseboth shot noise and constant additive noise. Or, the noise estimatorcould represent multiplicative noise that acts like additive noise butvaries linearly (or in some other mathematical function) with the imagesignal. Or, the noise estimator could make use of known variation in theimage generation process, such as optical vignetting, to parametricallymodify the noise estimate based on location within the 3-D image.

A possible application of the invention is to improve picture qualityfor still photographs. For this application, an imaging device collectsa number of short exposures, such as 8-12 exposures. This image sequenceis then processed with the above denoising method to denoise thesequence of exposures. After the denoising, a single still frame, suchas from the middle of the sequence is reported as a still image. Thismethod yields most of the benefit of a longer exposure, without themotion blur that the longer exposure would incur.

What is claimed is:
 1. A method of mitigating noise in source image datarepresenting pixels of a 3-D image, comprising: dividing the 3-D imageinto three-dimensional chunks of pixels; wherein each chunk is alignedfrom the same horizontal and vertical pixel positions of successiveimage frames; apodizing each chunk; performing a three-dimensionalFourier transform on each chunk, thereby producing transformed values ofthe pixels within each chunk and a three-dimensional spectrum of eachtransformed chunk; processing one or more transformed chunks to estimatea noise floor based on spectral values of the pixels within each chunk;determining a noise threshold based on the noise floor; filtering thespectrum of each transformed chunk with a denoising filter based on thenoise threshold; inverse transforming the transformed chunks; andrecombining the inverse transformed chunks into a denoised 3-D image. 2.The method of claim 1, wherein the three dimensions are vertical,horizontal, and time dimensions of image frames.
 3. The method of claim1, wherein the three dimensions are vertical, horizontal, and spatial.4. The method of claim 1, wherein the three dimensions are vertical,horizontal, and spectral.
 5. The method of claim 1, wherein each chunkhas equal numbers of pixels in two or more dimensions.
 6. The method ofclaim 1, wherein the denoising filter is a noise gating filter.
 7. Themethod of claim 1, wherein the denoising filter is a Weiner filter. 8.The method of claim 1, wherein the method is performed in near real timeas the 3-D image is received from an image data source over time.
 9. Themethod of claim 1, wherein the noise floor is further based onstatistics across image chunks of the Fourier spectrum in the sourceimage data.
 10. The method of claim 1, wherein the noise comprises shotnoise, whose amplitude varies proportionally to the square root of thelocal image value.
 11. The method of claim 10, wherein the noise flooris determined as a multiple of the median or some other percentile valueof each spectral component amplitude, when that component is consideredas a statistical ensemble across a number of chunks.
 12. The method ofclaim 1, wherein the noise comprises additive noise independent of pixelvalues.
 13. The method of claim 1, wherein the noise floor is determinedas a multiple of the median or some other percentile value of eachspectral component amplitude, when that component is considered as astatistical ensemble across a number of chunks.
 14. A method ofmitigating noise in source image data representing pixels of a 3-D imagethat comprises time-sequenced 2-D images, comprising: dividing the 3-Dimage into three-dimensional chunks of pixels, wherein the threedimensions are vertical, horizontal, and time dimensions; wherein eachchunk is aligned from the same horizontal and vertical pixel positionsof successive image frames; apodizing each chunk; performing athree-dimensional Fourier transform on each chunk, thereby producingtransformed values of the pixels within each chunk and athree-dimensional spectrum of each chunk; determining a noise threshold;filtering the spectrum of each chunk with a denoising filter based onthe noise threshold; inverse transforming the chunks; and recombiningthe chunks into a denoised image sequence.
 15. The method of claim 14,wherein the noise threshold is determined a priori.
 16. The method ofclaim 14, wherein the noise threshold is determined a posteriori fromspectral values of the pixels within each chunk.
 17. The method of claim16, wherein the noise threshold is further based on statistics acrossimage chunks of the Fourier spectrum in the source image data.
 18. Themethod of claim 14, wherein the denoising filter is a noise gatingfilter.
 19. The method of claim 14, wherein the denoising filter is aWeiner filter.
 20. The method of claim 14, wherein the method isperformed in near real time as the 3-D image is received from an imagedata source over time.